where \(\hat{L}\in \mathbb {R}^{\hat{c}\times \hat{c}}\)  with \(\hat{c} = \dim {\mathcal {V}_{1}}\) . As presented in [1]},
the reduced Laplacian \(\hat{L}\)  is again a symmetric Laplacian matrix. Correspondingly one can obtain the reduced incidence matrix \(\hat{D}\)  so that \(\hat{D}\hat{D}^T=\hat{L}\)  which means that we can define the equivalent reduced edges. As discussed in [1]} and [3]}, this Kron reduction process has the eigenvalues interlacing property where for every \(i=1,\dots ,\hat{c}\) ,
\(\begin{split}\lambda _i(L)\le \lambda _i(\hat{L})&\le \lambda _{i+c-\hat{c}}(L)\end{split}\) 
